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AMATYC Review Spring 2003
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The AMATYC Review

A refereed publication of the American Mathematical Association of Two-Year Colleges

Abstracts

Spring 2003 issue

Table of Contents

From the Editor
Feature Articles

Regular Articles

  • Notes From the Mathematical Underground by Alain Schremmer
  • Book ReviewEdited by Sandra DeLozier Coleman
  • Software Review Edited by Brian E. Smith
  • The Problems Section Edited by Stephen Plett and Robert Stong

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AMATYC Institutional Members

AMATYC Reviewers

AMATYC Executive Board and Committees

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College Algebra Reform Through Interdisciplinary Applications

William P. Fox, Jane E. Gower, George E. Schnibben, Jr., Elizabeth Gasque, and Richard D. West

William Fox is professor and chair at Francis Marion University. He received his PhD at Clemson University. His interests include mathematical modeling and real world applications. wfox@fmarion.edu

Jane Gower is an instructor in the mathematics department at Francis Marion University. She has an MS in mathematics education from North Carolina State University. Her interests include using Geometer's Sketchpad in trigonometry. jgower@fmarion.edu

George Schnibben is a professor in the mathematics department at Francis Marion University. He received his PhD in mathematics from Clemson University. His interests include mathematics history. gschnibben@fmarion.edu

Elizabeth Gasque is an assistant professor in the mathematics department at Francis Marion University. She received her PhD in mathematics education from the University of South Carolina. Her interests include T3 and preparing mathematics teachers for tomorrow. egasque@fmarion.edu

Richard West is an assistant professor in the mathematics department at Francis Marion University. He received his PhD in mathematics education from New York University. His interests include interdisciplinary applications in mathematics. rwest@fmarion.edu

FMU has been teaching college algebra since the school’s establishment in the early 1970s. We tried an experiment using applications and projects to motivate college algebra students. Our students had many positive comments about the experience. In this article, we give a few illustrative examples of the applications/projects used in our courses, and we share some student comments about the courses. Based on the overall positive experience, two new freshmen algebra courses were added using modeling and problem solving as their framework.

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College Algebra With Applications: Mathematics for Biology

Catherine M. Miller and Tamara B. Veenstra

Catherine M. Miller is professor of mathematics education at the University of Northern Iowa. She received her PhD from the University of Arizona. In addition to teaching classes for mathematics and mathematics education majors, she is interested in teacher cognition and pedagogical content knowledge. millerc@math.uni.edu

Tamara B. Veenstra is professor of mathematics at the University of Redlands in California. She received her PhD from Dartmouth College. Her research interests include many topics in number theory, especially student projects and educational issues related to teaching mathematics. tamara_veenstra@redlands.edu

Abstract not available

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The Effect of an Integrated Learning System on Two-Year College Students

Angela T. Barlow

Angela T. Barlow is assistant professor of mathematics at the State University of West Georgia. She received her PhD in mathematics education from Auburn University. In addition to teaching mathematics content courses for preservice K-8 teachers, she is interested in the role technology plays in the mathematics classroom. abarlow@westga.edu

The purpose of this study was to investigate the effectiveness of an integrated learning system in terms of algebra achievement, mathematical attitude, and mathematical anxiety. During Spring Semester 1999, students enrolled in elementary algebra at a community college participated in the study. The non-computer group received teacher-led instruction, while the computer group received instruction via Learning Logic, an integrated learning system designed to teach algebra.

At the beginning and at the end of the semester, students responded to the Descriptive Tests of Mathematics Skills (Elementary Algebra subtest), Aiken’s Mathematics Attitude Scale, and the Phobus, a mathematics anxiety scale. T tests analyzed the responses to each instrument. On the algebra pretest, the analysis found no significant difference between the computer group and the non-computer group. Low power was a concern for this analysis. On the post-test, however, the computer group scored significantly lower than the non-computer group. In terms of attitude for the computer group, a t test revealed no significant difference for a medium or large effect between pre-course attitude and post-course attitude. Similarly, for the computer group pre-course anxiety was not significantly different from post-course anxiety for a medium or large effect. Gender comparisons were made for the computer group in terms of achievement, attitude, and anxiety. While analyses revealed no significant differences, low power limited the interpretations of these analyses. Results suggested that Learning Logic, as implemented in this study, was not as effective as teacher-led instruction for teaching elementary algebra in this community college with regard to achievement.

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Adapting a Workshop Calculus Model to College Algebra: Instructional Challenges

Teri J. Murphy and Kathy Wahl

Teri J. Murphy is associate professor in the Department of Mathematics at the University of Oklahoma. tjmurphy@math.ou.edu

Kathy Wahl is a teaching associate at the University of Illinois at Urbana-Champaign. wahl@math.uiuc.edu

Abstract not available

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A Commonsense Approach to the Precalculus Presentation of Complex Numbers

Edwin F. Moats

Edwin F. Moats received his MS degree in mathematics from Western Washington University in Bellingham,WA, his MA in philosophy from Colorado State University, and his JD in law from Case Western Reserve University. He has been a community college mathematics, logic, and law instructor. His principal mathematical area of interest is analysis. edmoats@yahoo.com

Complex numbers are typically introduced to students in precalculus courses as a device necessary for finding roots of quadratic functions with negative discriminants. This approach is misleading to students, both historically and mathematically. In these presentations, students learn to competently perform algebraic manipulations to find roots of quadratics over the complex field, but they never learn what a complex number is.

Rarely is it mentioned that complex numbers are not quantities in the ordinary sense; that you cannot go to the grocery store and buy 3 + 2i dozen eggs. The student is inevitably left with the impression that complex numbers are "imaginary" in the sense of some amalgamation of magic and fiction, justly characterized by Leibnitz as "that amphibian between existence and nonexistence."1

My pedagogy of complex numbers is based upon on my conviction that students have a right to know the truth about the complex numbers: that they constitute the E2 vector space with the peculiar complex multiplication defined thereupon. The implementation of this pedagogy calls for deferring the presentation of complex numbers until students have a sufficient foundation. This means presenting complex numbers immediately after presenting E2 vectors, and presenting E2 vectors immediately after right triangle trigonometry.

1 Needham, T. (1997). Visual complex analysis. Oxford: Clarenden Press, p. 1.

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The Method of Gnomons and a New Scheme for Approximating Square Roots

Steven J. Kifowit

Steve Kifowit is associate professor of mathematics and chair of the Mathematics Department at Prairie State College. skifowit@prairiestate.edu

Abstract not available

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Entry-Level College Mathematics: Algebra or Modeling

Dan Kalman

Dan Kalman is associate professor of mathematics and statistics at American University. His interests include matrix theory, curriculum development, and instructional technology, particularly the Mathwright software. Kalman has won three writing awards from the MAA and is the author of a book on mathematical modeling. kalman@american.edu

In the past several years there has been increasing discussion of elementary mathematical modeling as an entry-level college course. In several institutions, modeling is now offered as an alternative to the more traditional college algebra course, and students can choose to complete a modeling course in fulfillment of a general education requirement. Of course, not everyone agrees with this approach. How can math teachers make an informed choice between college algebra and modeling? This paper argues that no such choice is necessary, for many of the instructional goals of the college algebra course can be addressed in a modeling course.

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The Cube Root Fallacy: Does (1 + z)3 = z3 Imply That 1 = 0?

John Mathews

John Mathews earned his doctorate at Michigan State University. He is currently teaching at California State University, Fullerton, where he is active in the areas of complex analysis and numerical analysis. Ongoing projects embrace the pedagogical use of computers to enhance the teaching of mathematics at the university level, and he is the author of two textbooks. mathews@fullerton.edu

Abstract not available

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Optimizing Functions of One Variable without Calculus

William B. Gearhart and Harris S. Shultz

William B. Gearhart received his BS degree in engineering physics and his PhD in applied mathematics from Cornell University. He is currently professor of mathematics at California State University, Fullerton. His research interests include approximation theory, numerical analysis, optimization theory, and mathematical modeling. wgearhart@fullerton.edu

Harris S. Shultz, professor of mathematics at California State University, Fullerton, received his BA degree in mathematics from Cornell University and his PhD in mathematics from Purdue University. He has directed numerous institutes for secondary mathematics teachers and has been a frequent contributor to The AMATYC Review. hshultz@fullerton.edu

Abstract not available

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